Question
$$\frac{3}{x}+4 = x+6$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -3 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{3}{x}+4 &= x+6&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{3}{x}+x\cdot4 &= xx+x\cdot6&& \text{cancel out the denominators} \\[1 em]3+4x &= x^2+6x&& \text{move all terms to the left hand side } \\[1 em]3+4x-x^2-6x &= 0&& \text{simplify left side} \\[1 em]-x^2-2x+3 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-2x+3 = 0 $ is a quadratic equation.
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